Primary line constants

The primary line constants are parameters that describe the characteristics of conductive transmission lines, such as pairs of copper wires, in terms of the physical electrical properties of the line. The primary line constants are only relevant to transmission lines and are to be contrasted with the secondary line constants, which can be derived from them, and are more generally applicable. The secondary line constants can be used, for instance, to compare the characteristics of a waveguide to a copper line, whereas the primary constants have no meaning for a waveguide. The constants are conductor resistance and inductance, and insulator capacitance and conductance, which are by convention given the symbols R, L, C, and G respectively. The constants are enumerated in terms of per unit length. The circuit representation of these elements requires a distributed-element model and consequently calculus must be used to analyse the circuit. The analysis yields a system of two first order, simultaneous linear partial differential equations which may be combined to derive the secondary constants of characteristic impedance and propagation constant. A number of special cases have particularly simple solutions and important practical applications. Low loss cable requires only L and C to be included in the analysis, useful for short lengths of cable. Low frequency applications, such as twisted pair telephone lines, are dominated by R and C only. High frequency applications, such as RF co-axial cable, are dominated by L and C. Lines loaded to prevent distortion need all four elements in the analysis, but have a simple, elegant solution. There are four primary line constants, but in some circumstances some of them are small enough to be ignored and the analysis can be simplified. These four, and their symbols and units are as follows: R and L are elements in series with the line (because they are properties of the conductor) and C and G are elements shunting the line (because they are properties of the dielectric material between the conductors).